For once, Wikipedia has a good article on primers: http://en.wikipedia.org/wiki/Primer_(paint)
In summary, paint has two functions: protection and decoration. Primer is really good at protection, so it makes sense to prime properly, with a specialist primer. Combined primer/undercoats inevitably compromise somewhere, usually on the ability to penetrate the wood.
The finish coat is just that, it's for the decoration.
If it's an outside wooden door I'd definitely go for a full three- or four-coat treatment. A good, expensive, aluminium primer, followed by one or two coats of undercoat, followed by one or two coats of top-coat. (But I live in the UK where conditions are horrid for wood -- very rainy, occasionally snowy, and dry and hot in the summer.)
In your case: you'll most likely be OK with two or three coats of combined paint/primer but be prepared for it to need another coat in three or four seasons. At that point a sand/recoat should be good.
Final tips: don't economise on paint quality, expensive brands invariably cover better and last longer. And, match manufacturers and chemistry if at all possible, as a paint "system" that matches will generally last longer. And, prepare, prepare, prepare!